CFT, Holography, and Causal Entropy Bound

TL;DR

This paper examines the validity of the causal entropy bound (CEB) in various conformal field theories (CFTs), demonstrating its consistency with holographic principles and large N bounds across different coupling regimes.

Contribution

It establishes the validity of the CEB for large N CFTs at certain temperature ranges and links it to holographic entropy bounds, bridging weak and strong coupling regimes.

Findings

CEB holds for large N CFTs below a specific temperature threshold.

CEB aligns with holographic entropy bounds in models with AdS duals.

The bound is consistent with large N gravity theories and the generalized second law.

Abstract

The causal entropy bound (CEB) is confronted with recent explicit entropy calculations in weakly and strongly coupled conformal field theories (CFTs) in arbitrary dimension $D$. For CFT's with a large number of fields, $N$, the CEB is found to be valid for temperatures not exceeding a value of order $M_P/N^{{1\over D-2}}$, in agreement with large $N$ bounds in generic cut-off theories of gravity, and with the generalized second law. It is also shown that for a large class of models including high-temperature weakly coupled CFT's and strongly coupled CFT's with AdS duals, the CEB, despite the fact that it relates extensive quantities, is equivalent to (a generalization of) a purely holographic entropy bound proposed by E. Verlinde.